Pipes A and B can fill a cistern in 12 hours, Pipes B and C can fill it in 14 hours and Pipes C and A can fill it in 15 hours. All three are opened together for 6 hours, then Pipes B and C are closed and Pipe A continues alone. Find the time taken by Pipe A to fill the remaining part of the cistern.

Raghav starts from Point A and drives 7 km towards west. He then takes a right turn, drives 4 km, turns right and drives 11 km. He then takes a right turn and drives 10 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)

If \((\cos\theta + \sin\theta) : (\cos\theta - \sin\theta) = (\sqrt{3} + 1) : (\sqrt{3} - 1), 0^\circ \lt \theta \lt 90^\circ\), then the value of \(\frac{\tan(\theta + 30^{\circ})}{\sec(\theta - 30^{\circ})}\) is:

If \(\tan^2 x = 1 - a^2\), then the value of \(\sec x + \tan^3 x \,\mathrm{cosec}\, x\) is:

A city's population decreases by 15% in the first year and by another 10% in the second year. In the third and fourth years, new development causes the population to grow by a constant rate of y% per year. If the population of the city, at the end of four years is 92.565% of the original size, what is the value of y?

A can complete a piece of work in 12 days and B can complete the same work in 18 days. They start working together. After 4 days, A leaves the work. In how many more days will B finish the remaining work?

The mode of a dataset is 25. Which of the following datasets has 25 as the unique mode?

A man has invested ₹57500 at a rate of 10% per annum simple interest for 3 years. Find the amount (in ₹) that he will receive after 3 years.

If 20% of k is 10 less than 3600% of 25, then k is: